ID software. Most known for making such classics as Wolfenstein 3D, Doom, and Quake, you'd have to have lived under a rock for the last 25 years or so to not know of this developer's accomplishments.

They were pioneers in game development, creating the legendary id tech proprietary game engine, which many engines today are based off of. 

Wolfenstein 3D was a simple maze shooter, but it was still something. Then Doom came along and really pushed the fps genre into mainstream attention. The game was also a technical marvel, as limitations of computer hardware at the time made game development harder. But iD worked with the limitations given to them and made a game that was ahead of it's time. The game used various techniques to work with the limitations and the result is a game that is still played and modded to this day.  I won't go into the various techniques the game used but look into them, it's really interesting stuff. Really showed how Doom worked with the limitations.

Quake. 

Ah yes, Quake. What Doom did for the FPS genre, as well as PC gaming, oh yeah, iD also pushed the PC as a legitimate gaming platform as well, but what Doom did for FPS and PC gaming, Quake did for multiplayer. 

More on that in a bit. 

Quake was also a technical marvel at the time, both graphically and, well technically, it was incredible. 3D environments, models, multiple floors, mouse look, fast paced gameplay, it was an incredible experience. It's engine is still influenced today, most engines used today are based off of Quake 2's engine.

Now, multiplayer. This game was revolutionary for online multiplayer. It's fast paced gameplay made for fun deathmatch. And then when Quake 3 came out, it was a standard. It started the esports craze which continues today. Were it not for Quake 3, Cod multiplayer wouldn't be a thing, most FPS wouldn't have taken off, and all the multiplayer focused games wouldn't be a thing.

The gaming industry owes a lot to iD Software, and that is why they're the most influential developer. They created an amazing engine, which is still improved and modified, kicked off the online multiplayer craze, and popularized the FPS genre. Their legacy will be remembered for years.